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Ali, Khalid K.; Raslan, K. R.; El-Danaf, Talaat S.

Numerical treatment for the coupled-BBM system. (English) Zbl 1356.65228

J. Mod. Methods Numer. Math. 7, No. 2, 67-79 (2016).
Summary: In the present paper, a numerical method is proposed for the numerical solution of a coupled Benjamin-Bona-Mahony (BBM) system with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms \(L_2\), \(L_\infty\) are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

Cited in 5 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

collocation method; quintic B-splines method; stability; error bound; coupled Benjamin-Bona-Mahony (BBM) system; solitary waves
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References:

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